A pr 2 00 5 ON GROMOV - HAUSDORFF CONVERGENCE FOR OPERATOR METRIC SPACES
نویسنده
چکیده
We introduce an analogue for Lip-normed operator systems of the second author’s order-unit quantum Gromov-Hausdorff distance and prove that it is equal to the first author’s complete distance. This enables us to consolidate the basic theory of what might be called operator Gromov-Hausdorff convergence. In particular we establish a completeness theorem and deduce continuity in quantum tori, Berezin-Toeplitz quantizations, and θ-deformations from work of the second author. We also show that approximability by Lip-normed matrix algebras is equivalent to 1-exactness of the underlying operator space and, by applying a result of Junge and Pisier, that for n ≥ 7 the set of isometry classes of n-dimensional Lipnormed operator systems is nonseparable.
منابع مشابه
2 3 N ov 2 00 4 ON GROMOV - HAUSDORFF CONVERGENCE FOR OPERATOR METRIC SPACES
We introduce an analogue for Lip-normed operator systems of the second author’s order-unit quantum Gromov-Hausdorff distance and prove that it is Lipschitz equivalent to the first author’s complete distance. This enables us to consolidate the basic theory of what might be called operator Gromov-Hausdorff convergence. In particular we establish a completeness theorem and deduce continuity in qua...
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